8.1: Motivation
We mentioned previously that given a subgroup \(H\) of \(G\text{,}\) we'd like to use \(H\) to get at some understanding of \(G\)'s entire structure. Recall that we've defined \(G/H\) to be the set of all left cosets of \(H\) in \(G\text{.}\) What we'd like to do now is equip \(G/H\) with some operation under which \(G/H\) is a group! The natural way to do this would be to define multiplication on \(G/H\) by
\begin{equation*} (aH)(bH)=abH \text{ for all } a,b\in G. \end{equation*}
Ok, so let's do that! But wait: we're defining this operation by referring to coset representatives, so we'd better make sure our operation is well-defined. Only it sadly turns out that in general this operation is not well-defined. For example:
Example \(\PageIndex{1}\)
Let \(H=\langle (12)\rangle\) in \(S_3\text{,}\) and let \(a=(13)\) and \(b=(132)\text{.}\) Let \(x=aH\) and \(y=bH\) in \(S_3/H\text{.}\) Then using the above-defined operation on \(G/H\) we'd have
\begin{equation*} xy=(aH)(bH)=abH=(13)(132)H=(23)H. \end{equation*}
But also \(x=(123)H\) and \(y=(23)H\text{,}\) so we'd also have
\begin{equation*} xy=((123)H)((23)H))=(123)(23)H=(12)H=H\neq (23)H. \end{equation*}
So this operation isn't well-defined.
The question for us now becomes: what conditions must hold for \(H\) in \(G\) in order for operation
\begin{equation*} (aH)(bH)=abH \end{equation*}
on \(G/H\) to be well-defined? It turns out that this operation is well-defined exactly when \(H\) is normal in \(G\text{!}\) We state this in the following theorem:
Theorem \(\PageIndex{1}\)
Let \(H\leq G\text{.}\) Then the operation
\begin{equation*} (aH)(bH)=abH \end{equation*}
on \(G/H\) is well-defined if and only if \(H \unlhd G\text{.}\)
- Proof
-
First, assume that the described operation is well-defined. Let \(a∈G\); we want to show that \(aH=Ha\).
Well, let \(x∈aH\). Then
\((xH)(a^{−1}H)=xa^{−1}H\)
and, since \(xH=aH\)
\((xH)(a^{−1}H)=(aH)(a^{−1}H)=aa^{−1}H=H\).
Since our operation on \(G/H\) is well-defined, this means that \(xa^{−1}H=H\), so \(xa^{−1}∈H\); thus, \(x∈Ha\). We conclude that \(aH⊆Ha\). The proof that \(Ha⊆aH\) is similar. So \(aH=Ha\), and thus, since \(a∈G\) was arbitrary, \(H\) is normal in \(G\).
Conversely, assume \(H⊴G\). Let \(a_1,a_2,b_1,b_2∈G\) with \(a_1H=a_2H\) and \(b_1H=b_2H\). We want to show that then \(a_1b_1H=a_2b_2H\), that is, that \((a_2b_2)^{−1}a_1b_1∈H\). Well, since \(a_1H=a_2H\) we have \(a_2^{−1}a_1∈H\). So
\((a_2b_2)^{−1}a_1b_1=b_2^{−1}(a_2^{−1}a_1)b_1∈b_2^{−1}Hb_1\).
Next, since \(H⊴G\), we have \(Hb_1=b_1H\), so \(b_2^{−1}Hb_1=b^{−1}_2b_1H\); but since \(b_1H=b_2H\), we have \(b_2^{−1}b_1∈H\), so \(b^{−1}_2b_1H=H\). Thus, \((a_2b_2)^{−1}a_1b_1∈H\), as desired.
Definition: Left Coset Multiplication
When \(H\unlhd G\text{,}\) the well-defined operation \((aH)(bH)=abH\) on \(G/H\) is called left coset multiplication .
It is clear that normal subgroups will be very important for us in studying group structures. We therefore spend some time looking at normal subgroups before returning to equipping \(G/H\) with a group structure.


Iodine
-
- Last updated
- Save as PDF
Learning Objectives
- Learn about the role of iodine
Recall the discovery of iodine and its use as a means of preventing goiter, a gross enlargement of the thyroid gland in the neck. Iodine is essential for the synthesis of thyroid hormone, which regulates basal metabolism, growth, and development. Low iodine levels and consequently hypothyroidism has many signs and symptoms including fatigue, sensitivity to cold, constipation, weight gain, depression, and dry, itchy skin and paleness. The development of goiter may often be the most visible sign of chronic iodine deficiency, but the consequences of low levels of thyroid hormone can be severe during infancy, childhood, and adolescence as it affects all stages of growth and development. Thyroid hormone plays a major role in brain development and growth and fetuses and infants with severe iodine deficiency develop a condition known as cretinism, in which physical and neurological impairment can be severe. The World Health Organization (WHO) estimates iodine deficiency affects over two billion people worldwide and it is the number-one cause of preventable brain damage worldwide.[1]
Dietary Reference Intakes for Iodine
| Age Group | RDA Males and Females mcg/day | UL |
|---|---|---|
| Infants (0–6 months) | 110* | - |
| Infants (7–12 months) | 130* | - |
| Children (1–3 years) | 90 | 200 |
| Children (4–8 years) | 120 | 300 |
| Children (9–13 years) | 150 | 600 |
| Adolescents (14–18 years) | 150 | 900 |
| Adults (> 19 years) | 150 | 1,100 |
*denotes Adequate Intake. Health Professional Fact Sheet: Iodine. National Institute of Health, Office of Dietary Supplements. https://ods.od.nih.gov/factsheets/Io...hProfessional/ . Updated June 24, 2011. Accessed November 10, 2017.
Dietary Sources of Iodine
The mineral content of foods is greatly affected by the soil from which it grew, and thus geographic location is the primary determinant of the mineral content of foods. For instance, iodine comes mostly from seawater so the greater the distance from the sea the lesser the iodine content in the soil.
| Food | Serving | Iodine (mcg) | Percent Daily Value |
|---|---|---|---|
| Seaweed | 1 g. | 16 to 2,984 | 11 to 1,989 |
| Cod fish | 3 oz. | 99 | 66 |
| Yogurt, low fat | 8 oz. | 75 | 50 |
| Iodized salt | 1.5 g. | 71 | 47 |
| Milk, reduced fat | 8 oz. | 56 | 37 |
| Ice cream, chocolate | ½ c. | 30 | 20 |
| Egg | 1 large | 24 | 16 |
| Tuna, canned | 3 oz. | 17 | 11 |
| Prunes, dried | 5 prunes | 13 | 9 |
| Banana | 1 medium | 3 | 2 |
Health Professional Fact Sheet: Iodine. National Institute of Health, Office of Dietary Supplements. https://ods.od.nih.gov/factsheets/Io...hProfessional/ . Updated June 24, 2011. Accessed November 10, 2017.
Footnotes
- World Health Organization. “Iodine Status Worldwide.” Accessed October 2, 2011. http://whqlibdoc.who.int/publication...9241592001.pdf .
Contributors and Attributions
-
University of Hawai’i at Mānoa Food Science and Human Nutrition Program : Allison Calabrese, Cheryl Gibby, Billy Meinke, Marie Kainoa Fialkowski Revilla, and Alan Titchenal


3.7: References- Unit III
-
- Last updated
- Save as PDF
- Miliann Kang, Donovan Lessard, Laura Heston, and Sonny Nordmarken
- University of Massachusetts Amherst via UMass Amherst Libraries
Allen, G. 1997. “The social and economic origins of genetic determinism: A case history of the American Eugenics Movement, 1900-1940 and its lessons for today.” Genetica . 99: 77-89.
American Civil Liberties Union. 2004. “Caught in the Net: The Impact of Drug Policies on Women and Families.” Accessed 1 April, 2017. http://www.aclu.org/files/images/ass...e431_23513.pdf
American Psychiatric Association. 2013. Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) . American Psychiatric Publishing.
Bettcher, Talia. 2007. “Evil Deceivers and Make‐Believers: On Transphobic Violence and the Politics of Illusion.” Hypatia 22 (3): 43-65.
Bourdieu, P. 1979.. Distinction: A Social Critique of the Judgment of Taste . Richard Nice (tr.). Harvard University Press, Cambridge, MA.
Bulhan, H. Frantz Fanon and the Psychology of Oppression . New York: University Press of Boston, 1985.
California Newsreel. 2008. Unnatural Causes…Is Inequality Making us Sick? Vital Pictures, Inc.
Campos, Paul. 2013. “Eugenics are Alive and Well in the United States.” Time . http://ideas.time.com/2013/07/10/eugenics-are-alive-and-well-in-the-united-states/ . Accessed 31 March, 2017.
Commonwealth Fund. 1997. The Commonwealth Fund Survey of the health of adolescent girls: Highlights and Methodology. New York, NY: The Commonwealth Fund.
Connell. R.W. 1987. Gender and Power: Society, the Person, and Sexual Politics . Palo Alto, CA: Stanford University Press.
Conrad, P. 2007. The Medicalization of Society: On the Transformation of Human Conditions into Treatable Disorder . Johns Hopkins University Press.
Davis, A. 2003 Are Prisons Obsolete? Open Media.
Foucault, Michel. 1978. The History of Sexuality: Volume I: The Will to Knowledge. New York, NY: Random House, Inc.
Gerstel, N. 2003. “Family” in The Blackwell Dictionary of Modern Social Thought, edited by W. Outhwaite . Blackwell Publishing, Ltd.
Glaze, Lauren E. and Laura M. Maruschak. 2010. “Bureau of Justice Statistics Special Report: Parents in Prison and their Minor children.” US Department of Justice. http://www.bjs.gov/content/pub/pdf/pptmc.pdf . Accessed 1 April, 2017.
Guterman, Lydia. 2011. “The Global Problem of Forced Sterilization.” Open Society Foundations. https://www.opensocietyfoundations.org/voices/global-problem-forced-sterilization . Accessed 31 March, 2017.
Jepperson, R. 1991. “Institutions, Institutional Effects, and Institutionalism.” Pp. 143–163 in The New Institutionalism in Organizational Analysis , edited by W. W. Powell, DiMaggio. Chicago: University of Chicago Press.
Kaeble, Danielle and Lauren Glaze. 2016. “Correctional Populations in the United States, 2015.” Bureau of Justice Statistics . US Department of Justice. https://www.bjs.gov/content/pub/pdf/cpus15.pdf . Accessed 1 April, 2017.
Kimmel, M. 2003. “The Gendered Media ”, in The Gendered Society, 2nd Edition, edited by Michael Kimmel. Oxford University Press.
Kilbourne, Jean. 2010. Killing Us Softly 4: Advertising’s Image of Women .
Kirk, G. and M. Okazawa-Rey. 2004. “Glossary of Terms in Common Use” in Women’s Lives: Multicultural Perspectives, 5th Edition, edited by Gwen Kirk and Margo Okazawa-Rey. New York, NY: McGraw-Hill.
____________. 2004. “Violence Against Women” in Women’s Lives: Multicultural Perspectives, 5th Edition, edited by Gwen Kirk and Margo Okazawa-Rey. New York, NY: McGraw-Hill.
LA Times. 2009. “Television viewing at all Time High.” http://articles.latimes.com/2009/feb/24/business/fi-tvwatching24 . Accessed 3 May, 2011.
Lombardo, Paul. 2011. A Century of Eugenics in America: From the Indiana Experiment to the Human Genome Era . Indianapolis: Indiana University Press.
Media Awareness Foundation. 2011. “Advertising Everywhere.” http://www.mediaawareness.ca/english/parents/marketing/advertising_everywhere.cfm . Accessed 3 May, 2011.
Miller, J. Mitchell. 2009. 21st Century Criminology: A Reference Handbook, Volume 1 . Sage Publications, Inc.
Mink, G. 2004. “Violating Women: Rights Abuses in the Welfare Police State”, Pp 350-358 in Women’s Lives, Multicultural Perspectives , Edited by Kirk, G. and M. Okazawa-Rey. New York, NY: McGraw-Hill.
Nielson Company. 2016. “The Total Audience Report: Q4 2015.” http://www.nielsen.com/us/en/insights/reports/2016/the-total-audience-report-q4-2015.html . Accessed 31 March, 2017.
Sabol, W. & H.C. West. 2010. Prisoners in 2009. NCJ 231675. Washington, D.C.: US Department of Justice, Bureau of Justice Statistics.
Sewell, W. 1992. “A Theory of Structure: Duality, Agency, and Transformation.” American Journal of Sociology 98: 1-29.
Shah, S. 2003. “The Orgasm Industry: Drug Companies Search for a Female Viagra”, Pp 328-331 in Sexual Lives: A Reader on the Theories and Realities of Human Sexualities , Edited by Robert Heasley and Betsy Crane. New York, NY: McGraw-Hill.
Smith, D. 1993. “The Standard North American Family: SNAF as an ideological code”. Journal of Family Issues 14(1): 50-65.
Stiglitz, J. 2011. “Of the 1%, By the 1%, for the 1%” in Vanity Fair , May 2011.
Transgender Europe. http://tgeu.org/issues/legal-gender-recognition/ . Accessed April 1, 2017.
Welch, Steven; Klassen, Cherisse; Borisova, Oxana; Clothier, Holly. 2013. “The DSM-5 controversies: How should psychologists respond?” Canadian Psychology/Psychologie canadienne . 54 (3): 166–175.
Weston, K. 1991. Families We Choose: Lesbians, Gays, Kinship . New York, NY: Columbia University Press.
United States Census Bureau. QuickFacts. https://www.census.gov/quickfacts/table/PST045216/00 . Accessed 1 April, 2017.


3.4: H.P. Lovecraft, “The Picture in the House” (1920)
H.P. Lovecraft, “The Picture in the House” (1920)
Jeanette A. Laredo
Born in Providence, Rhode Island in 1890, H.P. Lovecraft was an intelligent child whose early years would be tinged by tragedy. While he was still a newborn, his father Winfield Scott Lovecraft experienced mental deterioration due to untreated syphilis.  Lovecraft became obsessed with astrology growing up, an obsession nurtured by his grandmother. As a teenager, Lovecraft continued this interest in the cosmos and wrote writing monthly articles on astrology for the Providence Tribune. His later fiction was heavily influenced by the Gothic short stories of Edgar Allen Poe. Lovecraft experienced literary success in 1928 when the horror magazine Weird Tales purchased “The Call of Cthulhu” which featured a cosmic entity that would become the centerpiece of his unique Lovecraftian universe of fictional terror. “The Picture in the House” is more traditionally Gothic than Lovecraft’s later weird fiction and concerns a New England genealogist who encounters a threatening old man in a dilapidated house.
S earchers after horror haunt strange, far places. For them are the catacombs of Ptolemais, and the carven mausolea of the nightmare countries. They climb to the moonlit towers of ruined Rhine castles, and falter down black cobwebbed steps beneath the scattered stones of forgotten cities in Asia. The haunted wood and the desolate mountain are their shrines, and they linger around the sinister monoliths on uninhabited islands. But the true epicure in the terrible, to whom a new thrill of unutterable ghastliness is the chief end and justification of existence, esteems most of all the ancient, lonely farmhouses of backwoods New England; for there the dark elements of strength, solitude, grotesqueness and ignorance combine to form the perfection of the hideous.
Most horrible of all sights are the little unpainted wooden houses remote from travelled ways, usually squatted upon some damp grassy slope or leaning against some gigantic outcropping of rock. Two hundred years and more they have leaned or squatted there, while the vines have crawled and the trees have swelled and spread. They are almost hidden now in lawless luxuriances of green and guardian shrouds of shadow; but the small-paned windows still stare shockingly, as if blinking through a lethal stupor which wards off madness by dulling the memory of unutterable things.
In such houses have dwelt generations of strange people, whose like the world has never seen. Seized with a gloomy and fanatical belief which exiled them from their kind, their ancestors sought the wilderness for freedom. There the scions of a conquering race indeed flourished free from the restrictions of their fellows, but cowered in an appalling slavery to the dismal phantasms of their own minds. Divorced from the enlightenment of civilization, the strength of these Puritans turned into singular channels; and in their isolation, morbid self-repression, and struggle for life with relentless Nature, there came to them dark furtive traits from the prehistoric depths of their cold Northern heritage. By necessity practical and by philosophy stern, these folks were not beautiful in their sins. Erring as all mortals must, they were forced by their rigid code to seek concealment above all else; so that they came to use less and less taste in what they concealed. Only the silent, sleepy, staring houses in the backwoods can tell all that has lain hidden since the early days, and they are not communicative, being loath to shake off the drowsiness which helps them forget. Sometimes one feels that it would be merciful to tear down these houses, for they must often dream.
It was to a time-battered edifice of this description that I was driven one afternoon in November, 1896, by a rain of such chilling copiousness that any shelter was preferable to exposure. I had been travelling for some time amongst the people of the Miskatonic Valley in quest of certain genealogical data; and from the remote, devious, and problematical nature of my course, had deemed it convenient to employ a bicycle despite the lateness of the season. Now I found myself upon an apparently abandoned road which I had chosen as the shortest cut to Arkham, overtaken by the storm at a point far from any town, and confronted with no refuge save the antique and repellent wooden building which blinked with bleared windows from between two huge leafless elms near the foot of a rocky hill. Distant though it is from the remnant of a road, this house none the less impressed me unfavorably the very moment I espied it. Honest, wholesome structures do not stare at travellers so slyly and hauntingly, and in my genealogical researches I had encountered legends of a century before which biased me against places of this kind. Yet the force of the elements was such as to overcome my scruples, and I did not hesitate to wheel my machine up the weedy rise to the closed door which seemed at once so suggestive and secretive.
I had somehow taken it for granted that the house was abandoned, yet as I approached it I was not so sure, for though the walks were indeed overgrown with weeds, they seemed to retain their nature a little too well to argue complete desertion. Therefore instead of trying the door I knocked, feeling as I did so a trepidation I could scarcely explain. As I waited on the rough, mossy rock which served as a door-step, I glanced at the neighboring windows and the panes of the transom above me, and noticed that although old, rattling, and almost opaque with dirt, they were not broken. The building, then, must still be inhabited, despite its isolation and general neglect. However, my rapping evoked no response, so after repeating the summons I tried the rusty latch and found the door unfastened. Inside was a little vestibule with walls from which the plaster was falling, and through the doorway came a faint but peculiarly hateful odor. I entered, carrying my bicycle, and closed the door behind me. Ahead rose a narrow staircase, flanked by a small door probably leading to the cellar, while to the left and right were closed doors leading to rooms on the ground floor.
Leaning my cycle against the wall I opened the door at the left, and crossed into a small low-ceiled chamber but dimly lighted by its two dusty windows and furnished in the barest and most primitive possible way. It appeared to be a kind of sitting-room, for it had a table and several chairs, and an immense fireplace above which ticked an antique clock on a mantel. Books and papers were very few, and in the prevailing gloom I could not readily discern the titles. What interested me was the uniform air of archaism as displayed in every visible detail. Most of the houses in this region I had found rich in relics of the past, but here the antiquity was curiously complete; for in all the room I could not discover a single article of definitely post-revolutionary date. Had the furnishings been less humble, the place would have been a collector’s paradise.
As I surveyed this quaint apartment, I felt an increase in that aversion first excited by the bleak exterior of the house. Just what it was that I feared or loathed, I could by no means define; but something in the whole atmosphere seemed redolent of unhallowed age, of unpleasant crudeness, and of secrets which should be forgotten. I felt disinclined to sit down, and wandered about examining the various articles which I had noticed. The first object of my curiosity was a book of medium size lying upon the table and presenting such an antediluvian aspect that I marvelled at beholding it outside a museum or library. It was bound in leather with metal fittings, and was in an excellent state of preservation; being altogether an unusual sort of volume to encounter in an abode so lowly. When I opened it to the title page my wonder grew even greater, for it proved to be nothing less rare than Pigafetta’s account of the Congo region, written in Latin from the notes of the sailor Lopex and printed at Frankfurt in 1598. I had often heard of this work, with its curious illustrations by the brothers De Bry, hence for a moment forgot my uneasiness in my desire to turn the pages before me. The engravings were indeed interesting, drawn wholly from imagination and careless descriptions, and represented negroes with white skins and Caucasian features; nor would I soon have closed the book had not an exceedingly trivial circumstance upset my tired nerves and revived my sensation of disquiet. What annoyed me was merely the persistent way in which the volume tended to fall open of itself at Plate XII, which represented in gruesome detail a butcher’s shop of the cannibal Anziques. I experienced some shame at my susceptibility to so slight a thing, but the drawing nevertheless disturbed me, especially in connection with some adjacent passages descriptive of Anzique gastronomy.
I had turned to a neighboring shelf and was examining its meagre literary contents—an eighteenth century Bible, a “Pilgrim’s Progress” of like period, illustrated with grotesque woodcuts and printed by the almanack-maker Isaiah Thomas, the rotting bulk of Cotton Mather’s “Magnalia Christi Americana,” and a few other books of evidently equal age—when my attention was aroused by the unmistakable sound of walking in the room overhead. At first astonished and startled, considering the lack of response to my recent knocking at the door, I immediately afterward concluded that the walker had just awakened from a sound sleep, and listened with less surprise as the footsteps sounded on the creaking stairs. The tread was heavy, yet seemed to contain a curious quality of cautiousness; a quality which I disliked the more because the tread was heavy. When I had entered the room I had shut the door behind me. Now, after a moment of silence during which the walker may have been inspecting my bicycle in the hall, I heard a fumbling at the latch and saw the paneled portal swing open again.
In the doorway stood a person of such singular appearance that I should have exclaimed aloud but for the restraints of good breeding. Old, white-bearded, and ragged, my host possessed a countenance and physique which inspired equal wonder and respect. His height could not have been less than six feet, and despite a general air of age and poverty he was stout and powerful in proportion. His face, almost hidden by a long beard which grew high on the cheeks, seemed abnormally ruddy and less wrinkled than one might expect; while over a high forehead fell a shock of white hair little thinned by the years. His blue eyes, though a trifle bloodshot, seemed inexplicably keen and burning. But for his horrible unkemptness the man would have been as distinguished-looking as he was impressive. This unkemptness, however, made him offensive despite his face and figure. Of what his clothing consisted I could hardly tell, for it seemed to me no more than a mass of tatters surmounting a pair of high, heavy boots; and his lack of cleanliness surpassed description.
The appearance of this man, and the instinctive fear he inspired, prepared me for something like enmity; so that I almost shuddered through surprise and a sense of uncanny incongruity when he motioned me to a chair and addressed me in a thin, weak voice full of fawning respect and ingratiating hospitality. His speech was very curious, an extreme form of Yankee dialect I had thought long extinct; and I studied it closely as he sat down opposite me for conversation.
“Ketched in the rain, be ye?” he greeted. “Glad ye was nigh the haouse en’ hed the sense ta come right in. I calc’late I was asleep, else I’d a heerd ye—I ain’t as young as I uster be, an’ I need a paowerful sight o’ naps naowadays. Trav’lin fur? I hain’t seed many folks ‘long this rud sence they tuk off the Arkham stage.”
I replied that I was going to Arkham, and apologized for my rude entry into his domicile, whereupon he continued.
“Glad ta see ye, young Sir—new faces is scurce arount here, an’ I hain’t got much ta cheer me up these days. Guess yew hail from Bosting, don’t ye? I never ben thar, but I kin tell a taown man when I see ‘im—we hed one fer deestrick schoolmaster in ‘eighty-four, but he quit suddent an’ no one never heerd on ‘im sence—” here the old man lapsed into a kind of chuckle, and made no explanation when I questioned him. He seemed to be in an aboundingly good humor, yet to possess those eccentricities which one might guess from his grooming. For some time he rambled on with an almost feverish geniality, when it struck me to ask him how he came by so rare a book as Pigafetta’s “Regnum Congo.” The effect of this volume had not left me, and I felt a certain hesitancy in speaking of it, but curiosity overmastered all the vague fears which had steadily accumulated since my first glimpse of the house. To my relief, the question did not seem an awkward one, for the old man answered freely and volubly.
“Oh, that Afriky book? Cap’n Ebenezer Holt traded me thet in ‘sixty-eight—him as was kilt in the war.” Something about the name of Ebenezer Holt caused me to look up sharply. I had encountered it in my genealogical work, but not in any record since the Revolution. I wondered if my host could help me in the task at which I was laboring, and resolved to ask him about it later on. He continued.
 He got this in London, I guess—he uster like ter buy things at the shops. I was up ta his haouse onct, on the hill, tradin’ hosses, when I see this book. I relished the picters, so he give it in on a swap.  Donning these, he reached for the volume on the table and turned the pages lovingly.
“Ebenezer cud read a leetle o’ this—’tis Latin—but I can’t. I had two er three schoolmasters read me a bit, and Passon Clark, him they say got draownded in the pond—kin yew make anything outen it?” I told him that I could, and translated for his benefit a paragraph near the beginning. If I erred, he was not scholar enough to correct me; for he seemed childishly pleased at my English version. His proximity was becoming rather obnoxious, yet I saw no way to escape without offending him. I was amused at the childish fondness of this ignorant old man for the pictures in a book he could not read, and wondered how much better he could read the few books in English which adorned the room. This revelation of simplicity removed much of the ill-defined apprehension I had felt, and I smiled as my host rambled on:
“Queer haow picters kin set a body thinkin’. Take this un here near the front. Hey yew ever seed trees like thet, with big leaves a floppin’ over an’ daown? And them men—them can’t be niggers—they dew beat all. Kinder like Injuns, I guess, even ef they be in Afriky. Some o’ these here critters looks like monkeys, or half monkeys an’ half men, but I never heerd o’ nothin’ like this un.” Here he pointed to a fabulous creature of the artist, which one might describe as a sort of dragon with the head of an alligator.
“But naow I’ll show ye the best un—over here nigh the middle—”The old man’s speech grew a trifle thicker and his eyes assumed a brighter glow; but his fumbling hands, though seemingly clumsier than before, were entirely adequate to their mission. The book fell open, almost of its own accord and as if from frequent consultation at this place, to the repellent twelfth plate showing a butcher’s shop amongst the Anzique cannibals. My sense of restlessness returned, though I did not exhibit it. The especially bizarre thing was that the artist had made his Africans look like white men—the limbs and quarters hanging about the walls of the shop were ghastly, while the butcher with his axe was hideously incongruous. But my host seemed to relish the view as much as I disliked it.
“What d’ye think o’ this—ain’t never see the like hereabouts, eh? When I see this I telled Eb Holt, ‘That’s suthin’ ta stir ye up an’ make yer blood tickle.’ When I read in Scripter about slayin’—like them Midianites was slew—I kinder think things, but I ain’t got no picter of it. Here a body kin see all they is to it—I s’pose ’tis sinful, but ain’t we all born an’ livin’ in sin?—Thet feller bein’ chopped up gives me a tickle every time I look at ‘im—I hey ta keep lookin’ at ‘im—see whar the butcher cut off his feet? Thar’s his head on thet bench, with one arm side of it, an’ t’other arm’s on the other side o’ the meat block.”
As the man mumbled on in his shocking ecstasy the expression on his hairy, spectacled face became indescribable, but his voice sank rather than mounted. My own sensations can scarcely be recorded. All the terror I had dimly felt before rushed upon me actively and vividly, and I knew that I loathed the ancient and abhorrent creature so near me with an infinite intensity. His madness, or at least his partial perversion, seemed beyond dispute. He was almost whispering now, with a huskiness more terrible than a scream, and I trembled as I listened.
 D’ye know, young Sir, I’m right sot on this un here. Arter I got the book off Eb I uster look at it a lot, especial when I’d heerd Passon Clark rant o’ Sundays in his big wig. Onct I tried suthin’ funny—here, young Sir, don’t git skeert—all I done was ter look at the picter afore I kilt the sheep for market—killin’ sheep was kinder more fun arter lookin’ at it—” The tone of the old man now sank very low, sometimes becoming so faint that his words were hardly audible. I listened to the rain, and to the rattling of the bleared, small-paned windows, and marked a rumbling of approaching thunder quite unusual for the season. Once a terrific flash and peal shook the frail house to its foundations, but the whisperer seemed not to notice it.
“Killin’ sheep was kinder more fun—but d’ye know, ‘twan’t quite satisfyin’. Queer haow a cravin’ gits a holt on ye—As ye love the Almighty, young man, don’t tell nobody, but I swar ter Gawd thet picter begun to make me hungry fer victuals I couldn’t raise nor buy—here, set still, what’s ailin’ ye?—I didn’t do nothin’, only I wondered haow ‘twud be ef I did—They say meat makes blood an’ flesh, an’ gives ye new life, so I wondered ef ‘twudn’t make a man live longer an’ longer ef ’twas more the same—” But the whisperer never continued. The interruption was not produced by my fright, nor by the rapidly increasing storm amidst whose fury I was presently to open my eyes on a smoky solitude of blackened ruins. It was produced by a very simple though somewhat unusual happening.
The open book lay flat between us, with the picture staring repulsively upward. As the old man whispered the words “more the same” a tiny splattering impact was heard, and something showed on the yellowed paper of the upturned volume. I thought of the rain and of a leaky roof, but rain is not red. On the butcher’s shop of the Anzique cannibals a small red spattering glistened picturesquely, lending vividness to the horror of the engraving. The old man saw it, and stopped whispering even before my expression of horror made it necessary; saw it and glanced quickly toward the floor of the room he had left an hour before. I followed his glance, and beheld just above us on the loose plaster of the ancient ceiling a large irregular spot of wet crimson which seemed to spread even as I viewed it.  A moment later came the titanic thunderbolt of thunderbolts; blasting that accursed house of unutterable secrets and bringing the oblivion which alone saved my mind.


1.12: Genes and Chromatin in Eukaryotes
-
- Last updated
- Save as PDF
- Ying Liu
- City College of San Francisco
Chromosomes and chromatin are a uniquely eukaryotic association of DNA with more or less protein. Bacterial DNA (and prokaryotic DNA generally) is relatively ‘naked’ – not visibly associated with protein.
The electron micrograph of an interphase cell (below) reveals that the chromatin can itself exist in various states of condensation.
Chromatin is maximally condensed during mitosis, forming chromosomes. During interphase, chromatin exists in more or less condensed forms, called Heterochromatin and euchromatin respectively. Transition between these chromatin forms involve changes in the amounts and types of proteins bound to the chromatin, and can that can occur during gene regulation, i.e., when genes are turned on or off. Active genes tend to be in the more dispersed euchromatin so that enzymes of replication and transcription have easier access to the DNA. Genes that are inactive in transcription are heterochromatic, obscured by additional chromatin proteins present in heterochromatin. We’ll be looking at some experiments that demonstrate this in a later chapter.
We can define three levels of chromatin organization in general terms:
1. DNA wrapped around histone proteins form nucleosomes in a "beads on a string" structure.
2. Multiple nucleosomes coil (condense), forming 30 nm fiber (solenoid) structures.
3. Higher-order packing of the 30 nm fiber leads to formation of metaphase chromosomes seen in mitosis & meiosis.
The levels of chromatin structure were determined in part by selective isolation and extraction of interphase cell chromatin, followed by selective chemical extraction of chromatin components. The steps are:
· Nuclei are first isolated from the cells.
· The nuclear envelope gently ruptured so as not to physically disrupt chromatin structure.
· the chromatin can be gently extracted by one of several different chemical treatments (high salt, low salt, acid...).
The levels of chromatin structure are illustrated below.
Salt extraction dissociates most of the proteins from the chromatin. When a low salt extract is centrifuged and the pellet resuspended, the remaining chromatin looks like beads on a string . DNA-wrapped nucleosomes are the beads, which are in turn linked by uniform lengths of metaphorical DNA “string’ ( # 1 in the illustration above). A high salt chromatin extract appears as a coil of nucleosomes, or 30 nm solenoid fiber (# 2 above). Other extraction protocols revealed other aspects of chromatin structure shown in #s 3 and 4 above. Chromosomes seen in metaphase of mitosis are the ‘highest order’, most condensed form of chromatin.
The 10 nm filament of nucleosome ‘beads-on-a-string’ remaining after a low salt extraction can be seen in an electron microscope as shown below.
When these nucleosome necklaces were digested with the enzyme deoxyribonuclease ( DNAse ), the DNA between the ‘beads’ was degraded, leaving behind shortened 10nm filaments after a short digest period, or just single beads the beads after a longer digestion (below).
Roger Kornberg (son of Nobel Laureate Arthur Kornberg who discovered the first DNA polymerase enzyme of replication) participated in the discovery and characterization of nucleosomes while he was still a post-doc! Electrophoresis of DNA extracted from these digests revealed nucleosomes separated by a “linker” DNA stretch of about 80 base pairs. DNA extracted from the nucleosomes was about 147 base pairs long. This is the DNA that had been wrapped around the proteins of the nucleosome.
After separating all of the proteins from nucleosomal DNA, five proteins were identified (illustrated below).
Histones are basic proteins containing many lysine and arginine amino acids. Their positively charged side chains enable these amino acids bind the acidic, negatively charged phosphodiester backbone of double helical DNA. The DNA wraps around an octamer of histones (2 each of 4 of the histone proteins) to form the nucleosome . About a gram of histones is associated with each gram of DNA. After a high salt chromatin extraction, the structure visible in the electron microscope is the 30nm solenoid, the coil of nucleosomes modeled in the figure below.
As shown above, simply increasing the salt concentration of an already extracted nucleosome preparation will cause the ‘necklace’ to fold into the 30nm solenoid structure.
173 Chromatin Structure: Dissecting Chromatin
As you might guess, an acidic extraction of chromatin should selectively remove the basic histone proteins, leaving behind an association of DNA with non-histone proteins. This proved to be the case. An electron micrograph of the chromatin remnant after an acid extraction of metaphase chromosomes is shown on the next page.
DNA freed of the regularly spaced histone-based nucleosomes, loops out, away from the long axis of the chromatin. Dark material along this axis is a protein scaffolding that makes up what’s left after histone extraction. Much of this protein is topoisomerase , an enzyme that prevents DNA from breaking apart under the strain of replication.


77: Why Good People Turn Bad Online (Vince)
Gaia Vince
#technology #analysis #causalargument #systemanalysis #sharedvalues #research
On the evening of 17 February 2018, Professor Mary Beard posted on Twitter a photograph of herself crying. The eminent University of Cambridge classicist, who has almost 200,000 Twitter followers, was distraught after receiving a storm of abuse online. This was the reaction to a comment she had made about Haiti. She also tweeted: “I speak from the heart (and of cource I may be wrong).
In the days that followed, Beard received support from several high-profile people. Greg Jenner, a fellow celebrity historian, tweeted about his own experience of a Twitterstorm: “I’ll always remember how traumatic it was to suddenly be hated by strangers. Regardless of morality – I may have been wrong or right in my opinion – I was amazed (later, when I recovered) at how psychologically destabilising it was to me.”
Those tweeting support for Beard – irrespective of whether they agreed with her initial tweet that had triggered the abusive responses – were themselves then targeted. And when one of Beard’s critics, fellow Cambridge academic Priyamvada Gopal, a woman of Asian heritage, set out her response to Beard’s original tweet in an online article, she received her own torrent of abuse.
There is overwhelming evidence that women and members of ethnic minority groups are disproportionately the target of Twitter abuse. Where these identity markers intersect, the bullying can become particularly intense, as experienced by black female MP Diane Abbott, who alone received nearly half of all the abusive tweets sent to female MPs during the run-up to the 2017 UK general election. Black and Asian female MPs received on average 35 per cent more abusive tweets than their white female colleagues even when Abbott was excluded from the total.
The constant barrage of abuse, including death threats and threats of sexual violence, is silencing people, pushing them off online platforms and further reducing the diversity of online voices and opinion. And it shows no sign of abating. A survey last year found that 40 percent of American adults had personally experienced online abuse, with almost half of them receiving severe forms of harassment, including physical threats and stalking. 70 percent of women described online harassment as a “major problem”.
The business models of social media platforms, such as YouTube and Facebook, promote content that is more likely to get a response from other users because more engagement means better opportunities for advertising. But this has a consequence of favouring divisive and strongly emotive or extreme content, which can in turn nurture online “bubbles” of groups who reflect and reinforce each other’s opinions, helping propel the spread of more extreme content and providing a niche for “fake news”. In recent months, researchers have revealed many ways that various vested interests, including Russian operatives, have sought to manipulate public opinion by infiltrating social media bubbles.
Our human ability to communicate ideas across networks of people enabled us to build the modern world. The internet offers unparalleled promise of cooperation and communication between all of humanity. But instead of embracing a massive extension of our social circles online, we seem to be reverting to tribalism and conflict, and belief in the potential of the internet to bring humanity together in a glorious collaborating network now begins to seem naive. While we generally conduct our real-life interactions with strangers politely and respectfully, online we can be horrible. How can we relearn the collaborative techniques that enabled us to find common ground and thrive as a species?
“Don’t overthink it, just press the button!”
I click an amount, impoverishing myself in an instant, and quickly move on to the next question, aware that we’re all playing against the clock. My teammates are far away and unknown to me. I have no idea if we’re all in it together or whether I’m being played for a fool, but I press on, knowing that the others are depending on me.
I’m playing in a so-called public goods game at Yale University’s Human Cooperation Lab. The researchers here use it as a tool to help understand how and why we cooperate, and whether we can enhance our prosocial behaviour.
Over the years, scientists have proposed various theories about why humans cooperate so well that we form strong societies. The evolutionary roots of our general niceness, most researchers now believe, can be found in the individual survival advantage humans experience when we cooperate as a group. I’ve come to New Haven, Connecticut, in a snowy February, to visit a cluster of labs where researchers are using experiments to explore further our extraordinary impulse to be nice to others even at our own expense.
The game I’m playing, on Amazon’s Mechanical Turk online platform, is one of the lab’s ongoing experiments. I’m in a team of four people in different locations, and each of us is given the same amount of money to play with. We are asked to choose how much money we will contribute to a group pot, on the understanding that this pot will then be doubled and split equally among us.
This sort of social dilemma, like all cooperation, relies on a certain level of trust that the others in your group will be nice. If everybody in the group contributes all of their money, all the money gets doubled, redistributed four ways, and everyone doubles their money. Win–win!
“But if you think about it from the perspective of an individual,” says lab director David Rand, “for each dollar that you contribute, it gets doubled to two dollars and then split four ways – which means each person only gets 50 cents back for the dollar they contributed.”
Even though everyone is better off collectively by contributing to a group project that no one could manage alone – in real life, this could be paying towards a hospital building, or digging a community irrigation ditch – there is a cost at the individual level. Financially, you make more money by being more selfish.
Rand’s team has run this game with thousands of players. Half of them are asked, as I was, to decide their contribution rapidly – within 10 seconds – whereas the other half are asked to take their time and carefully consider their decision. It turns out that when people go with their gut, they are much more generous than when they spend time deliberating.
“There is a lot of evidence that cooperation is a central feature of human evolution,” says Rand. Individuals benefit, and are more likely to survive, by cooperating with the group. And being allowed to stay in the group and benefit from it is reliant on our reputation for behaving cooperatively.
“In the small-scale societies that our ancestors were living in, all our interactions were with people that you were going to see again and interact with in the immediate future,” Rand says. That kept in check any temptation to act aggressively or take advantage and free-ride off other people’s contributions. “It makes sense, in a self-interested way, to be cooperative.”
Cooperation breeds more cooperation in a mutually beneficial cycle. Rather than work out every time whether it’s in our long-term interests to be nice, it’s more efficient and less effort to have the basic rule: be nice to other people. That’s why our unthinking response in the experiment is a generous one.
Throughout our lives, we learn from the society around us how cooperative to be. But our learned behaviours can also change quickly.
Those in Rand’s experiment who play the quickfire round are mostly generous and receive generous dividends, reinforcing their generous outlook. Whereas those who consider their decisions are more selfish, resulting in a meagre group pot, reinforcing an idea that it doesn’t pay to rely on the group. So, in a further experiment, Rand gave some money to people who had played a round of the game. They were then asked how much they wanted to give to an anonymous stranger. This time, there was no incentive to give; they would be acting entirely charitably.
 The people who had got used to cooperating in the first stage gave twice as much money in the second stage as the people who had got used to being selfish did. “So we’re affecting people’s internal lives and behaviour,” Rand says. “The way they behave even when no one’s watching and when there’s no institution in place to punish or reward them.”
Rand’s team have tested how people in different countries play the game, to see how the strength of social institutions – such as government, family, education and legal systems – influences behaviour. In Kenya, where public sector corruption is high , players initially gave less generously to the stranger than players in the US, which has less corruption. This suggests that people who can rely on relatively fair social institutions behave in a more public-spirited way; those whose institutions are less reliable are more protectionist. However, after playing just one round of the cooperation-promoting version of the public goods game, the Kenyans’ generosity equalled the Americans’. And it cut both ways: Americans who were trained to be selfish gave a lot less.
So is there something about online social media culture that makes some people behave meanly? Unlike ancient hunter-gatherer societies , which rely on cooperation and sharing to survive and often have rules for when to offer food to whom across their social network, social media have weak institutions. They offer physical distance, relative anonymity and little reputational or punitive risk for bad behaviour: if you’re mean, no one you know is going to see.
I trudge a couple of blocks through driving snow to find Molly Crockett’s Psychology Lab, where researchers are investigating moral decision-making in society. One area they focus on is how social emotions are transformed online, in particular moral outrage. Brain-imaging studies show that when people act on their moral outrage, their brain’s reward centre is activated – they feel good about it. This reinforces their behaviour, so they are more likely to intervene in a similar way again. So, if they see somebody acting in a way that violates a social norm, by allowing their dog to foul a playground, for instance, and they publicly confront the perpetrator about it, they feel good afterwards. And while challenging a violator of your community’s social norms has its risks – you may get attacked – it also boosts your reputation.
In our relatively peaceful lives, we are rarely faced with outrageous behaviour, so we rarely see moral outrage expressed. Open up Twitter or Facebook and you get a very different picture. Recent research shows that messages with both moral and emotional words are more likely to spread on social media – each moral or emotional word in a tweet increases the likelihood of it being retweeted by 20 per cent.
“Content that triggers outrage and that expresses outrage is much more likely to be shared,” Crockett says. What we’ve created online is “an ecosystem that selects for the most outrageous content, paired with a platform where it’s easier than ever before to express outrage”.
Unlike in the offline world, there is no personal risk in confronting and exposing someone. It only takes a few clicks of a button and you don’t have to be physically nearby, so there is a lot more outrage expressed online. And it feeds itself. “If you punish somebody for violating a norm, that makes you seem more trustworthy to others, so you can broadcast your moral character by expressing outrage and punishing social norm violations,” Crockett says. “And people believe that they are spreading good by expressing outrage – that it comes from a place of morality and righteousness.
“When you go from offline – where you might boost your reputation for whoever happens to be standing around at the moment – to online, where you broadcast it to your entire social network, then that dramatically amplifies the personal rewards of expressing outrage.”
This is compounded by the feedback people get on social media, in the form of likes and retweets and so on. “Our hypothesis is that the design of these platforms could make expressing outrage into a habit, and a habit is something that’s done without regard to its consequences – it’s insensitive to what happens next, it’s just a blind response to a stimulus,” Crockett explains.
“I think it’s worth having a conversation as a society as to whether we want our morality to be under the control of algorithms whose purpose is to make money for giant tech companies,” she adds.
On the upside, the lower costs of expressing outrage online have allowed marginalised, less-empowered groups to promote causes that have traditionally been harder to advance. Moral outrage on social media played an important role in focusing attention on the sexual abuse of women by high-status men. And in February 2018, Florida teens railing on social media against yet another high-school shooting in their state helped to shift public opinion , as well as shaming a number of big corporations into dropping their discount schemes for National Rifle Association members.
“I think that there must be ways to maintain the benefits of the online world,” says Crockett, “while thinking more carefully about redesigning these interactions to do away with some of the more costly bits.”
Someone who’s thought a great deal about the design of our interactions in social networks is Nicholas Christakis, director of Yale’s Human Nature Lab, located just a few more snowy blocks away. His team studies how our position in a social network influences our behaviour, and even how certain influential individuals can dramatically alter the culture of a whole network.
The team is exploring ways to identify these individuals and enlist them in public health programmes that could benefit the community. In Honduras, they are using this approach to influence vaccination enrolment and maternal care, for example. Online, such people have the potential to turn a bullying culture into a supportive one.
Corporations already use a crude system of identifying so-called Instagram influencers to advertise their brands for them. But Christakis is looking not just at how popular an individual is, but also their position in the network and the shape of that network. In some networks, like a small isolated village, everyone is closely connected and you’re likely to know everyone at a party; in a city, by contrast, people may be living more closely by as a whole, but you are less likely to know everyone at a party there. How thoroughly interconnected a network is affects how behaviours and information spread around it, he explains.
“If you take carbon atoms and you assemble them one way, they become graphite, which is soft and dark. Take the same carbon atoms and assemble them a different way, and it becomes diamond, which is hard and clear. These properties of hardness and clearness aren’t properties of the carbon atoms – they’re properties of the collection of carbon atoms and depend on how you connect the carbon atoms to each other,” he says. “And it’s the same with human groups.”
Christakis has designed software to explore this by creating temporary artificial societies online. “We drop people in and then we let them interact with each other and see how they play a public goods game, for example, to assess how kind they are to other people.”
Then he manipulates the network. “By engineering their interactions one way, I can make them really sweet to each other, work well together, and they are healthy and happy and they cooperate. Or you take the same people and connect them a different way and they’re mean jerks to each other and they don’t cooperate and they don’t share information and they are not kind to each other.”
In one experiment, he randomly assigned strangers to play the public goods game with each other. In the beginning, he says, about two-thirds of people were cooperative. “But some of the people they interact with will take advantage of them and, because their only option is either to be kind and cooperative or to be a defector, they choose to defect because they’re stuck with these people taking advantage of them.
Christakis turned this around simply by giving each person a little bit of control over who they were connected to after each round. “They had to make two decisions: am I kind to my neighbours or am I not; and do I stick with this neighbour or do I not.” The only thing each player knew about their neighbours was whether each had cooperated or defected in the round before. “What we were able to show is that people cut ties to defectors and form ties to cooperators, and the network rewired itself and converted itself into a diamond-like structure instead of a graphite-like structure.” In other words, a cooperative prosocial structure instead of an uncooperative structure.
In an attempt to generate more cooperative online communities, Christakis’s team have started adding bots to their temporary societies. He takes me over to a laptop and sets me up on a different game. In this game, anonymous players have to work together as a team to solve a dilemma that tilers will be familiar with: each of us has to pick from one of three colours, but the colours of players directly connected to each other must be different. If we solve the puzzle within a time limit, we all get a share of the prize money; if we fail, no one gets anything. I’m playing with at least 30 other people. None of us can see the whole network of connections, only the people we are directly connected to – nevertheless, we have to cooperate to win.
I’m connected to two neighbours, whose colours are green and blue, so I pick red. My left neighbour then changes to red so I quickly change to blue. The game continues and I become increasingly tense, cursing my slow reaction times. I frequently have to switch my colour, responding to unseen changes elsewhere in the network, which send a cascade of changes along the connections. Time’s up before we solve the puzzle, prompting irate responses in the game’s comments box from remote players condemning everyone else’s stupidity. Personally, I’m relieved it’s over and there’s no longer anyone depending on my cackhanded gaming skills to earn money.
Christakis tells me that some of the networks are so complex that the puzzle is impossible to solve in the timeframe. My relief is shortlived, however: the one I played was solvable. He rewinds the game, revealing for the first time the whole network to me. I see now that I was on a lower branch off the main hub of the network. Some of the players were connected to just one other person, but most were connected to three or more. Thousands of people from around the world play these games on Amazon Mechanical Turk, drawn by the small fee they earn per round. But as I’m watching the game I just played unfold, Christakis reveals that three of these players are actually planted bots. “We call them ‘dumb AI’,” he says.
His team is not interested in inventing super-smart AI to replace human cognition. Instead, the plan is to infiltrate a population of smart humans with dumb-bots to help the humans help themselves.
“We wanted to see if we could use the dumb-bots to get the people unstuck so they can cooperate and coordinate a little bit more – so that their native capacity to perform well can be revealed by a little assistance,” Christakis says. He found that if the bots played perfectly, that didn’t help the humans. But if the bots made some mistakes, they unlocked the potential of the group to find a solution.
“Some of these bots made counter-intuitive choices. Even though their neighbours all had green and they should have picked orange, instead they also picked green.” When they did that, it allowed one of the green neighbours to pick orange, “which unlocks the next guy over, he can pick a different colour and, wow, now we solve the problem”. Without the bot, those human players would probably all have stuck with green, not realising that was the problem. “Increasing the conflicts temporarily allows their neighbours to make better choices.”
By adding a little noise into the system, the bots helped the network to function more efficiently. Perhaps a version of this model could involve infiltrating the newsfeeds of partisan people with occasional items offering a different perspective, helping to shift people out of their social media comfort-bubbles and allow society as a whole to cooperate more.
Much antisocial behaviour online stems from the anonymity of internet interactions – the reputational costs of being mean are much lower than offline. Here, bots may also offer a solution.  A typical bot response to a racist tweet would be: “Hey man, just remember that there are real people who are hurt when you harass them with that kind of language.” Simply cultivating a little empathy in such tweeters reduced their racist tweets almost to zero for weeks afterwards.
Another way of addressing the low reputational cost for bad behaviour online is to engineer in some form of social punishment. One game company, League of Legends, did that by introducing a “Tribunal” feature, in which negative play is punished by other players. The company reported that 280,000 players were “reformed” in one year, meaning that after being punished by the Tribunal they had changed their behaviour and then achieved a positive standing in the community. Developers could also build in social rewards for good behaviour, encouraging more cooperative elements that help build relationships.
Researchers are already starting to learn how to predict when an exchange is about to turn bad – the moment at which it could benefit from pre-emptive intervention. “You might think that there is a minority of sociopaths online, which we call trolls, who are doing all this harm,” says Cristian Danescu-Niculescu-Mizil, at Cornell University’s Department of Information Science. “What we actually find in our work is that ordinary people, just like you and me, can engage in such antisocial behaviour. For a specific period of time, you can actually become a troll. And that’s surprising.”
It’s also alarming. I mentally flick back through my own recent tweets, hoping I haven’t veered into bullying in some awkward attempt to appear funny or cool to my online followers. After all, it can be very tempting to be abusive to someone far away, who you don’t know, if you think it will impress your social group.
Danescu-Niculescu-Mizil has been investigating the comments sections below online articles. He identifies two main triggers for trolling: the context of the exchange – how other users are behaving – and your mood. “If you’re having a bad day, or if it happens to be Monday, for example, you’re much more likely to troll in the same situation,” he says. “You’re nicer on a Saturday morning.”
After collecting data, including from people who had engaged in trolling behaviour in the past, Danescu-Niculescu-Mizil built an algorithm that predicts with 80 per cent accuracy when someone is about to become abusive online. This provides an opportunity to, for example, introduce a delay in how fast they can post their response. If people have to think twice before they write something, that improves the context of the exchange for everyone: you’re less likely to witness people misbehaving, and so less likely to misbehave yourself.
The good news is that, in spite of the horrible behaviour many of us have experienced online, the majority of interactions are nice and cooperative. Justified moral outrage is usefully employed in challenging hateful tweets. A recent British study looking at anti-Semitism on Twitter found that posts challenging anti-Semitic tweets are shared far more widely than the anti-Semitic tweets themselves. Most hateful posts were ignored or only shared within a small echo chamber of similar accounts. Perhaps we’re already starting to do the work of the bots ourselves.
As Danescu-Niculescu-Mizil points out, we’ve had thousands of years to hone our person-to-person interactions, but only 20 years of social media. “Offline, we have all these cues from facial expressions to body language to pitch… whereas online we discuss things only through text. I think we shouldn’t be surprised that we’re having so much difficulty in finding the right way to discuss and cooperate online.”
As our online behaviour develops, we may well introduce subtle signals, digital equivalents of facial cues, to help smooth online discussions. In the meantime, the advice for dealing with online abuse is to stay calm, it’s not your fault. Don’t retaliate but block and ignore bullies, or if you feel up to it, tell them to stop. Talk to family or friends about what’s happening and ask them to help you. Take screenshots and report online harassment to the social media service where it’s happening, and if it includes physical threats, report it to the police.
If social media as we know it is going to survive, the companies running these platforms are going to have to keep steering their algorithms, perhaps informed by behavioural science, to encourage cooperation rather than division, positive online experiences rather than abuse. As users, we too may well learn to adapt to this new communication environment so that civil and productive interaction remains the norm online as it is offline.
“I’m optimistic,” Danescu-Niculescu-Mizil says. “This is just a different game and we have to evolve.”
References
The New Statesman tracked abusive tweets sent to women MPs in the run-up to the 2017 UK general election.
A 2017 Pew Research Center survey showed that 41 percent of Americans have experienced online harassment.
Researchers at University College London investigated what hunter-gatherers can tell us about social networks.
Research published in PNAS showed that emotion influences how content spreads online.
In 2016, Ars Technica reported a study showing how Twitter bots can reduce racist slurs.
Community Security Trust, a charity that protects British Jews from anti-Semitism, published a report about anti-Semitic content on Twitter in 2018.
____________________
Gaia Vince is a journalist, broadcaster and author specialising in science, the environment and social issues. Her article first appeared in Mosaic .
Why Good People Turn Bad Online by Gaia Vince is licensed under a Creative Commons Attribution 4.0 International License .


11.17: Exercise- Averaging with a Custom aSME Time Window
-
- Last updated
- Save as PDF
The series of scripts in the previous exercise produce a dataset for each participant that is ready for averaging. In the present exercise, we’ll compute the averaged ERPs, including calculating aSME for a custom time window of 110-150 ms (the measurement window for the N170). We’ll then create a grand average across participants and plot it. Finally, we’ll print a summary of the aSME values to the Command Window.
Go ahead an open the script ( Step6_averaging_and_SME.m ) and take a look at it. As usual, the script begins by defining a set of variables that will be used later in the script. It also opens a file named ERPset_files.txt . This file will be used when we make the grand average. When we made grand averages in previous chapters, we loaded all the single-participant ERPsets into ALLERP and then told the grand averaging routine which of these ERPsets to include the grand average. However, it’s sometimes more convenient just to work with one ERPSet at a time, save the ERPsets as files on the hard drive, and not keep all the ERPsets loaded in memory. In this case, we can send the grand averaging routine a list of the filenames of the ERPsets, which are themselves stored in a text file. This is what ERPset_files.txt is used for in the present script. I could have just loaded all the ERPsets into ALLERP, but I wanted to demonstrate this alternative approach and show you how to open a text file and write to it.
The main loop in the script begins by loading the dataset that was created by the previous script, which is all ready for averaging. The next few lines define the custom aSME time window. This information is stored in a data structure called a DQ_spec ( data quality specification ). This structure both defines the time windows prior to obtaining the data quality measures and stores the data quality measures once they’ve been calculated. It’s a little complicated, so ERPLAB provides a routine called make_DQ_spec to create it.
We use this routine to create a variable named custom_aSME_spec . There are potentially many different types of data quality metrics that can be stored in a DQ_spec variable. The first metric stored in a DQ_spec structure is a measure of the baseline noise. The second is the standard error of the mean at each individual time point. The third is the aSME. It’s possible for you to define additional types, the most common of which is the bSME (bootstrapped SME). Here, we’re going to use aSME, but we’re going to specific a custom time window for the aSME calculation so that we get an aSME value that corresponds to our N170 measurement window (110–150 ms). We do this by finding out how many time windows have already been defined by default and then adding a new one.
The next step is to call the averaging routine ( pop_averager ), sending it the custom_aSME_spec variable that we just created so that it will compute the aSME for our custom time window (along with the default time windows). This routine returns an ERPset that we store in the ERP variable. We then create a name for the ERPset and save the ERPset to a file on the hard drive. We also save the name of this file (including the path) in the ERPset_files.txt file so that we have it when we make the grand average later.
The ERP variable includes a field named ERP.dataquality that stores the data quality metrics that were calculated during the averaging process. The script shows how you can grab the aSME values from ERP.dataquality for the channel we will ultimately use to score the N170 amplitude (PO8, Channel 27). For each subject, we get an array of four aSME values for this channel, one for each of the four bins. We store this in a two-dimensional array named aSME_custom_values, which has one dimension for subjects and another dimension for bins. The aSME data inside ERP.dataquality are stored in a 3D array with dimensions of channels, time ranges, and bins, and we use a Matlab function called squeeze to convert this 3D array into the 1D array of values for each bin for the current subject:
aSME_custom_values(subject,:) = squeeze(ERP.dataquality(where_aSME).data(measurement_channel,custom_entry_index,:));
When you’re first learning to write scripts in Matlab, you’ll probably find that you frequently get confused about how arrays work and when you need to use a function like squeeze to obtain the desired results. I still sometimes get confused, and I often make mistakes when writing code that operates on complicated arrays. But I’ve learned how in interpret Matlab’s error messages, and I often search the Internet for solutions. I also recommend getting a good Matlab book and spending some time learning the logic behind how Matlab operates on arrays. As I mentioned earlier, my lab uses a book called Matlab for Behavioral Scientists (Rosenbaum et al., 2014).
After the main loop finishes, the script makes a grand average using the filenames stored in ERPset_files.txt . It then plots the grand average so that you can see how to script the plotting routine ( pop_ploterps ).
Finally, the script prints out the custom aSME values that we saved in the variable named aSME_custom_values for each participant. It also prints the mean across participants for each bin, along with the RMS (root mean square). The RMS is like the mean, but it does a better job of capturing how the noise level from the individual participants will impact the variability in N170 amplitude scores across participants, the effect size, and the statistical power (see Luck et al., 2021). I recommend taking a look at the aSME values for each participant and then looking at their EEG and ERPs to see if you can understand why some participants have worse (larger) aSME values than others.
The aSME quantifies the data quality for the mean voltage within a given time window, so it’s most directly useful when you’re scoring amplitude using the mean voltage (which is how we scored N170 amplitude in the ERP CORE paper). If you’re using some other scoring method (e.g., peak amplitude, fractional peak latency), you need to use a more complicated method called bootstrapping to obtain the SME values. You’ll also need to use bootstrapping if you’ll be obtaining scores from difference waves or if you apply any other kind of processing to the ERP data after averaging but before scoring (e.g., filtering or channel operations). ERPLAB currently requires scripting to compute bootstrapped SME values, and of the example scripts at the end of Chapter 10 demonstrate how to do this. Chapter 10 also contains a script that demonstrates how to obtain behavioral data.


20.5: Motivating Students
selected template will load here
This action is not available.
As Lao Tzu observed, “You can no more teach without the learner than a merchant can sell without a willing buyer.” Follow the ARCS motivation model to ensure that students will be motivated to learn.
Note
Motivate learners because without motivation learning is unlikely to occur.
As described by Keller, motivation can be enhanced through addressing the four attributes of Attention, Relevance, Confidence, and Satisfaction (ARCS). Try to include all of the attributes since each alone may not maintain student motivation. Your learner analysis may have provided useful information for motivating students.
You should build motivational strategies into the materials throughout the instructional design process. This is challenging since each learner is an individual with unique interests, experiences, and goals.
Note
Carefully determine your motivational strategies since each learner has unique interests, experiences, and goals.
Gain attention and then sustain it. You can gain attention by using human-interest examples, arousing emotions such as by showing a peer being wheeled into an ambulance, presenting personal information, challenging the learner, providing an interesting problem to solve, arousing the learner’s curiosity, showing exciting video or animation sequences, stating conflicting information, using humour, asking questions, and presenting a stimulus change that can be as simple as an audio beep. One way to sustain attention is by making the learning highly interactive. Figure \(\PageIndex{1}\) shows an attention-grabbing strategy.
Relevance helps the student to want to learn the material. For example, when teaching adult students how to solve percent problems, having them calculate the gratuity on a restaurant bill may be more relevant than a problem that compares two person’s ages. You can provide relevance through testimonials, illustrative stories, simulations, practical applications, personal experience, and relating the material to present or future values or needs. Relevance is also useful in helping to sustain attention.
For material to be perceived as being relevant, you must strive to match the learner’s expectations to the material you provide.
If students are confident that they can master the material, they will be much more willing to attempt the instruction. You will need to convince students with low confidence that they can be successful. You can do this through presenting the material in small incremental steps, or even by stating how other similar students have succeeded. Tasks should seem achievable rather than insurmountable.
You should also convince students who are overconfident that there is material that they need to learn. You can do this by giving a challenging pre-test or presenting difficult questions.
Satisfaction provides value for learning the material. Satisfaction can be intrinsic from the pleasure or value of the activity itself, extrinsic from the value or importance of the activity’s result, for social reasons such as pleasing people who’s opinions are important to them, for achievement goals such as the motive to be successful or avoid failure, or a combination of these. Examples of intrinsic satisfaction include the joy or challenge of learning, increased confidence, positive outcomes, and increased feelings of self-worth. Examples of extrinsic satisfaction include monetary rewards, praise, a certificate, avoidance of discomfort or punishment for not doing it, and unexpected rewards. Some evidence suggests that extrinsic motivation, such as a certificate for completing a course, does not last over time. Nonetheless, it is better to assume that some students need extrinsic motivation. To be safe, try to provide your learners with both intrinsic, which should have more of the focus, and extrinsic rewards. If the intrinsic motivation is high for all learners, you will not need to plan as much for extrinsic motivation. Note that satisfaction can be provided by enabling learners to apply the skills they have gained in a meaningful way.
Remember to let the students know that the material to be learned is important. Consider increasing extrinsic motivation through quizzes and tests.


10.6: Euler's second law for special cases
We now discuss a few special types of motion that can be analysed with Euler’s second law.
10.6.1 Pure translation
In the case of pure translation, we have no angular acceleration \(\overrightarrow{\boldsymbol{\alpha}}=\overrightarrow{\mathbf{0}}\), which is the case if the moment of all external forces with respect to the CoM is zero \(\left(\overrightarrow{\boldsymbol{M}}_{C, G}=\overrightarrow{\mathbf{0}}\right)\). This situation is for instance valid for the moments generated in a constant gravitational field, or when constraint equations prevent rotations. Then Equation 10.22 becomes:
\[\begin{align} & \text { If : } \sum_{i} \overrightarrow{\boldsymbol{M}}_{C, i / G}=I_{G, z z} \alpha_{C} \hat{\boldsymbol{k}}=\overrightarrow{\mathbf{0}} \tag{10.47} \label{10.47}\\[4pt] & \sum_{i} M_{C, i / P, 2 D} \hat{\boldsymbol{k}}=\overrightarrow{\boldsymbol{r}}_{G / P} \times\left(m_{\mathrm{tot}} \overrightarrow{\boldsymbol{a}}_{G}\right)=\overrightarrow{\boldsymbol{r}}_{G / P} \times\left(\sum_{i} \overrightarrow{\boldsymbol{F}}_{i, \mathrm{ext}}\right)\end{align}\]
It can be seen that once it is known that \(\overrightarrow{\boldsymbol{\alpha}}_{C}=\overrightarrow{\boldsymbol{0}}\), Euler’s second law on the moments does not provide additional useful information beyond Euler’s first law that determines the acceleration of the CoM of the rigid body via \(\sum_{i} \overrightarrow{\boldsymbol{F}}_{i, \mathrm{ext}}=m_{\mathrm{tot}} \overrightarrow{\boldsymbol{a}}_{G}\).
10.6.2 Pure rotation around the centre of mass
It is interesting to consider the situation where the term \(m_{\text {tot }} \overrightarrow{\boldsymbol{a}}_{G}=\overrightarrow{\boldsymbol{0}}\) is zero because the sum of forces on the rigid body is zero, since it significantly simplifies Equation 10.22, with the disappearance of the term \(\overrightarrow{\boldsymbol{r}}_{G / P} \times\left(m_{\mathrm{tot}} \overrightarrow{\boldsymbol{a}}_{G}\right)\).
\[\begin{align} \text { If : } \sum_{i} \overrightarrow{\boldsymbol{F}}_{\mathrm{i}, \mathrm{ext}} & =m_{\mathrm{tot}} \overrightarrow{\boldsymbol{a}}_{G}=\overrightarrow{\mathbf{0}} \tag{10.48} \label{10.48}\\[4pt] \text { Then }: \sum_{i} M_{C, i / P, 2 D} \hat{\boldsymbol{k}} & =I_{G, z z} \alpha_{C} \hat{\boldsymbol{k}} \tag{10.49} \label{10.49}\end{align}\]
We thus find in Equation 10.49 that the CoM of the rigid body does not accelerate and the acting moments purely cause an angular acceleration \(\alpha_{C}\) of the rigid body.
10.6.3 Couple
We saw in the previous subsection that a special situation arises if the sum of the forces acting on a system is zero, since then \(\overrightarrow{\boldsymbol{a}}_{G}=\overrightarrow{\mathbf{0}}\). Such a combination of forces is called a couple, and if there are only two forces it is called a simple couple.
\(A\) simple couple consists of two forces \(\overrightarrow{\boldsymbol{F}}_{A}=-\overrightarrow{\boldsymbol{F}}_{B}\) that are equal in magnitude, and opposite in direction such that \(\overrightarrow{\boldsymbol{F}}_{A}+\overrightarrow{\boldsymbol{F}}_{B}=\overrightarrow{\mathbf{0}}\), while the forces have different points of action, such that their resultant moment is not zero.
Besides simple couples, that consist of two forces, there is also a more general definition of a couple, that can consist of more than two forces.
A couple consists of a number of \(N\) forces for which the sum of forces is zero, that generate a resultant moment on a system. So \(\sum_{i=1}^{N} \overrightarrow{\boldsymbol{F}}_{i, \mathrm{ext}}=\overrightarrow{\mathbf{0}}\).
According to Euler’s second law, a couple only influences the angular acceleration \(\alpha\) of a rigid body, it does not contribute to the acceleration \(\overrightarrow{\boldsymbol{a}}_{G}\) of the CoM because the sum of the forces is zero. The effect of a couple is therefore also called a pure moment or couple moment.
Another useful property of a couple is that its resultant pure moment is independent of the choice of the location of the reference point \(P\), as we will derive now.
Consider a simple couple generated by two force vectors with \(\overrightarrow{\boldsymbol{F}}_{A}=-\overrightarrow{\boldsymbol{F}}_{B}\) acting on points \(A\) and \(B\). The moment of this couple with respect to a reference point \(P\) is given by:
\[\begin{align} \overrightarrow{\boldsymbol{M}}_{\text {couple }} & =\overrightarrow{\boldsymbol{r}}_{A / P} \times \overrightarrow{\boldsymbol{F}}_{A}+\overrightarrow{\boldsymbol{r}}_{B / P} \times \overrightarrow{\boldsymbol{F}}_{B} \tag{10.50} \label{10.50}\\[4pt] & =\overrightarrow{\boldsymbol{r}}_{A / P} \times \overrightarrow{\boldsymbol{F}}_{A}-\overrightarrow{\boldsymbol{r}}_{B / P} \times \overrightarrow{\boldsymbol{F}}_{A} \tag{10.51} \label{10.51}\\[4pt] & =\left(\left(\overrightarrow{\boldsymbol{r}}_{A}-\overrightarrow{\boldsymbol{r}}_{P}\right)-\left(\overrightarrow{\boldsymbol{r}}_{B}-\overrightarrow{\boldsymbol{r}}_{P}\right)\right) \times \overrightarrow{\boldsymbol{F}}_{A} \tag{10.52} \label{10.52}\\[4pt] & =\overrightarrow{\boldsymbol{r}}_{A / B} \times \overrightarrow{\boldsymbol{F}}_{A} \tag{10.53} \label{10.53}\end{align}\]
From this equation we see that the couple vector \(\overrightarrow{\boldsymbol{M}}_{\text {couple }}\) is independent of the choice of the reference point \(P\) and only depends on the force vectors of the couple and their points of action \(\overrightarrow{\boldsymbol{r}}_{A}\) and \(\overrightarrow{\boldsymbol{r}}_{B}\).
10.6.4 Pure rotation around a fixed axis
Let us now consider pure rotation of a rigid body \(C\) about a fixed axis \(P\) parallel to the \(z\)-axis, which does not translate \(\left(\overrightarrow{\boldsymbol{a}}_{P}=\overrightarrow{\boldsymbol{v}}_{P}=\overrightarrow{\boldsymbol{0}}\right)\). We choose point \(P\) as reference point. There is no translation of this point, only the angular acceleration of the rigid body \(\alpha\). As a consequence we have from Equation 9.29 that \(\overrightarrow{\boldsymbol{a}}_{G}=\overrightarrow{\boldsymbol{\alpha}} \times \overrightarrow{\boldsymbol{r}}_{G / P}-\omega^{2} \overrightarrow{\boldsymbol{r}}_{G / P}\). Substituting this into Equation 10.22 we obtain:
\[\begin{align} & \text { If : } \overrightarrow{\boldsymbol{a}}_{P}=\overrightarrow{\boldsymbol{v}}_{P}=\overrightarrow{\mathbf{0}} \tag{10.54} \label{10.54}\\[4pt] \sum_{i} M_{C, i / P, 2 D} \hat{\boldsymbol{k}}= & m_{\mathrm{tot}} \overrightarrow{\boldsymbol{r}}_{G / P} \times\left(\overrightarrow{\boldsymbol{\alpha}} \times \overrightarrow{\boldsymbol{r}}_{G / P}-\omega^{2} \overrightarrow{\boldsymbol{r}}_{G / P}\right)+I_{G, z z} \alpha_{C} \hat{\boldsymbol{k}} \\[4pt] = & m_{\mathrm{tot}} \rho_{G / P} \hat{\boldsymbol{\rho}} \times\left(\alpha \hat{\boldsymbol{k}} \times \rho_{G / P} \hat{\boldsymbol{\rho}}\right)+I_{G, z z} \alpha_{C} \hat{\boldsymbol{k}} \\[4pt] = & \left(m_{\mathrm{tot}} \rho_{G / P}^{2}+I_{G, z z}\right) \alpha \hat{\boldsymbol{k}} \tag{10.55} \label{10.55}\\[4pt] = & I_{P, z z} \alpha \hat{\boldsymbol{k}} \tag{10.56} \label{10.56}\end{align}\]
In the last step we used the parallel axes theorem \(I_{z z, P}=m_{\mathrm{tot}} \rho_{G / P}^{2}+I_{G, z z}\), where \(\rho_{G / P}\) is the smallest distance between the parallel axes through \(G\) and \(P\). The conclusion from Equation 10.56 is that for a rigid body \(C\) that rotates in-plane around a fixed axis \(P\) : the sum of the moments with respect to the fixed axis \(P\) equals the product of the moment of inertia \(I_{z z, P}\) and the angular acceleration \(\alpha_{C}\) of the rigid body \(C\).


2.2.2: Two Equations for Each Relationship
Lesson
Let's investigate the equations that represent proportional relationships.
Exercise \(\PageIndex{1}\): Missing Figures
Here are the second and fourth figures in a pattern.
- What do you think the first and third figures in the pattern look like?
- Describe the 10th figure in the pattern.
Exercise \(\PageIndex{2}\): Meters and Centimeters
There are 100 centimeters (cm) in every meter (m).
| length (m) | length (cm) |
|---|---|
| \(1\) | \(100\) |
| \(0.94\) | |
| \(1.67\) | |
| \(57.24\) | |
| \(x\) |
| length (cm) | length (m) |
|---|---|
| \(100\) | \(1\) |
| \(250\) | |
| \(78.2\) | |
| \(123.9\) | |
| \(y\) |
- Complete each of the tables.
- For each table, find the constant of proportionality.
- What is the relationship between these constants of proportionality?
- For each table, write an equation for the proportional relationship. Let \(x\) represent a length measured in meters and \(y\) represent the same length measured in centimeters.
Are you ready for more?
- How many cubic centimeters are there in a cubic meter?
- How do you convert cubic centimeters to cubic meters?
- How do you convert the other way?
Exercise \(\PageIndex{3}\): Filling a Water Cooler
It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let \(w\) be the number of gallons of water in the cooler after \(t\) minutes.
-
Which of the following equations represent the relationship between \(w\) and \(t\)? Select
all
that apply.
- \(w=1.6t\)
- \(w=0.625t\)
- \(t=1.6w\)
- \(t=0.625w\)
- What does 1.6 tell you about the situation?
- What does 0.625 tell you about the situation?
- Priya changed the rate at which water flowed through the faucet. Write an equation that represents the relationship of \(w\) and \(t\) when it takes 3 minutes to fill the cooler with 1 gallon of water.
- Was the cooler filling faster before or after Priya changed the rate of water flow? Explain how you know.
Exercise \(\PageIndex{4}\): Feeding Shrimp
At an aquarium, a shrimp is fed \(\frac{1}{5}\) gram of food each feeding and is fed 3 times each day.
- How much food does a shrimp get fed in one day?
-
Complete the table to show how many grams of food the shrimp is fed over different numbers of days.
number of days food in grams \(1\) \(7\) \(30\) Table \(\PageIndex{3}\)
Figure \(\PageIndex{1}\) - What is the constant of proportionality? What does it tell us about the situation?
- If we switched the columns in the table, what would be the constant of proportionality? Explain your reasoning.
- Use \(d\) for number of days and \(f\) for amount of food in grams that a shrimp eats to write two equations that represent the relationship between \(d\) and \(f\).
- If a tank has 10 shrimp in it, how much food is added to the tank each day?
- If the aquarium manager has 300 grams of shrimp food for this tank of 10 shrimp, how many days will it last? Explain or show your reasoning.
Summary
If Kiran rode his bike at a constant 10 miles per hour, his distance in miles, \(d\), is proportional to the number of hours, \(t\), that he rode. We can write the equation \(d=10t\). With this equation, it is easy to find the distance Kiran rode when we know how long it took because we can just multiply the time by 10.
We can rewrite the equation:
\[\begin{aligned} d&=10t \\ \left(\frac{1}{10}\right) d&=t\\t&=\left(\frac{1}{10}\right)d \end{aligned}\nonumber\]
This version of the equation tells us that the amount of time he rode is proportional to the distance he traveled, and the constant of proportionality is \(\frac{1}{10}\). That form is easier to use when we know his distance and want to find how long it took because we can just multiply the distance by \(\frac{1}{10}\).
When two quantities \(x\) and \(y\) are in a proportional relationship, we can write the equation \(y=kx\) and say, “\(y\) is proportional to \(x\).” In this case, the number \(k\) is the corresponding constant of proportionality. We can also write the equation \(x=\frac{1}{k}y\) and say, “\(x\) is proportional to \(y\).” In this case, the number \(\frac{1}{k}\) is the corresponding constant of proportionality. Each one can be useful depending on the information we have and the quantity we are trying to figure out.
Practice
Exercise \(\PageIndex{5}\)
The table represents the relationship between a length measured in meters and the same length measured in kilometers.
| meters | kilometers |
|---|---|
| \(1,000\) | \(1\) |
| \(3,500\) | |
| \(500\) | |
| \(75\) | |
| \(1\) | |
| \(x\) |
- Complete the table.
- Write an equation for converting the number of meters to kilometers. Use \(x\) for number of meters and \(y\) for number of kilometers.
Exercise \(\PageIndex{6}\)
Concrete building blocks weigh 28 pounds each. Using \(b\) for the number of concrete blocks and \(w\) for the weight, write two equations that relate the two variables. One equation should begin with \(w=\) and the other should begin with \(b=\).
Exercise \(\PageIndex{7}\)
A store sells rope by the meter. The equation \(p=0.8L\) represents the price \(p\) (in dollars) of a piece of nylon rope that is \(L\) meters long.
- How much does the nylon rope cost per meter?
- How long is a piece of nylon rope that costs $1.00?
Exercise \(\PageIndex{8}\)
The table represents a proportional relationship. Find the constant of proportionality and write an equation to represent the relationship.
| \(a\) | \(y\) |
|---|---|
| \(2\) | \(\frac{2}{3}\) |
| \(3\) | \(1\) |
| \(10\) | \(\frac{10}{3}\) |
| \(12\) | \(4\) |
Constant of proportionality: __________
Equation: \(y=\)
(From Unit 2.2.1)
Exercise \(\PageIndex{9}\)
On a map of Chicago, 1 cm represents 100 m. Select all statements that express the same scale.
- 5 cm on the map represents 50 m in Chicago.
- 1 mm on the map represents 10 m in Chicago.
- 1 km in Chicago is represented by 10 cm the map.
- 100 cm in Chicago is represented by 1 m on the map.
(From Unit 1.2.2)


28.1.2: Code and Output
selected template will load here
This action is not available.
Incredibly, that’s about it. Everything else in this book is going to concern what to type in those Code cells and how to interpret its output.
From now on, whenever I give example Python code in this book, I’ll write it like this
Code \(\PageIndex{1}\) (Python):
founding = 1776
usa_age = 2021 - founding
print("Our country is {} years old!".format(usa_age))
That means “this stuff goes in a Code cell of a Notebook.” When I write the corresponding output (i.e., what gets printed on the page immediately below the code cell when “Run All” is chosen from the “Cell” menu), I’ll write it like this:
| Our country is 245 years old!
That vertical bar means “this stuff is the printed result of executing the code cell.” Easy enough. Onward!


3.3: Questions to Guide Your Reading
1. How did the geography of South Asia (India) impact its history?
2. What are the limits of our knowledge of Harappan Civilization?
3. How did kingdoms form during the Vedic Age?
4. Describe the varna and caste systems.
5. Explain the early historical origins and basic beliefs of Hinduism and Buddhism. How do these religious traditions change over time?
6. How was the Mauryan Empire governed?
7. How was India impacted by other regions of Afro-Eurasia, and how did it impact them?
8. Why is the Gupta period sometimes described as a classical age?
9. What are the characteristics of early medieval India?
10. Explain the history of the formation of Muslim states in India.


1.16.4: Ion-Water Interactions
The seminal paper in this subject was published in 1933 by Bernal and Fowler [1]. These authors drew attention to the possible impact of ions on water - water interactions in aqueous solutions beyond nearest-neighbour water molecules. The paper is also notable for the fact that the authors in their examination of the properties of ice, water and salt solutions did not use the term ‘hydrogen bond’ [2]. At that time there was much debate concerning the nature of this interaction bearing in mind that the ‘valency’ of hydrogen is unity. Rather Bernal and Fowler concluded that ‘the unique properties of water are due to a structure of an extended complex characterized by tetrahedral co-ordination’.
Verwey drew attention to the importance of the interactions between an ion and near-neighbor water molecules in aqueous solution [3,4], these water molecules often being described as ‘electrostricted ‘ by strong ion- solvent dipole interactions. Solvent water plays an important role in the control of partial molar entropies of ions in aqueous solutions [5] and transfer entropies of ions from aqueous to non-aqueous solvents [6].
A major landmark was a paper published by Frank and Evans who developed the concept that solutes, polar and apolar, have an important impact on water - water interactions in aqueous solutions [7]. In the development of models for ionic hydration, a distinction is drawn between hydrophilic and hydrophobic ions. Hydrophilic ions (alkali metal cations and halide anions) have strong attractive interactions with neighbouring dipolar water molecules. Neutron scattering data reveal important information concerning the arrangement of water molecules contiguous to ions [8-10].
For example in the case of chloride ions, the \(\mathrm{Cl} – \mathrm{~H} - 0\) configuration is essentially linear. Nevertheless, there is clear evidence, albeit often secondary, that strong water - ion interactions have an impact on water - water interactions beyond the immediate hydration sheath. Viscosity data indicate that ions, such as iodide and potassium, have a structure breaking effect. The cospheres, for these ions, are drawn, showing two parts [11,12]; an inner zone A and an outer zone B [11].
In zone A, ion - water dipole interactions are strong, leading to the general description ionichydration [12]. An indication of the structure of hydrated ions in solution emerges from X-ray crystallographic studies [13]. In the case of \(\mathrm{KF}.4\mathrm{H}_{2}\mathrm{O}\), the structure comprises \(\mathrm{K}^{+} \left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\) and \(\mathrm{F}^{-} \left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\) octahedra; the \(\mathrm{K}^{+} -\mathrm{O}\) distance is \(0.279 \mathrm{~nm}\). Kebarle showed that mass spectrometry could be used to study ion - water interactions and, interestingly, step-wise hydration in the gas phase [14].
If a given ion in aqueous solution is indeed surrounded by two zones identified as zones A band B, the expectation is that ion - ion interactions in solution will reflect the impact of these structural features [15].
In the context of the impact of zone B, the suggestion was that with increase in size of ions so zone B should increase. Hence the expectation was that, for example, the partial molar isobaric heat capacity of tetra-n-butylammonium bromide in aqueous solution would be large in magnitude and negative in sign. Such not the case; the sign is positive [16,17]. A link was therefore established between the hydration characteristic of tetra-alkylammoniun ions and the structures of the corresponding salt hydrates [18]; e.g. tetra-iso-amylammonium fluoride hydrate, \((\text{iso}-\mathrm{Am})_{4}\mathrm{N}^{+} \mathrm{~F}^{-} 38 \mathrm{~H}_{2}\mathrm{O}\) [19]. Generally, therefore, tetra-alkylammonium ions of \(\mathrm{C}_{4} - \mathrm{~C}_{9}\) carboxylates and tri-alkylsulphonium ions are often identified as hydrophobic where the interaction between these ions and neighboring water molecules is weak. [20-32]. Interestingly, constricting the alkyl chains to form azoniaspiroalkane cations diminishes the hydrophobic character [33,34]. The impact of replacing a hydrophobic terminal group in \(\mathrm{R}_{4}\mathrm{N}^{+}\) ions by a hydrophilic group on the properties of aqueous solutions is dramatic and offers an interesting insight into the role of ion – water interactions [35]. In contrast Finney and co-workers report that neutron diffraction data for aqueous solutions, containing \(\mathrm{Me}_{4}\mathrm{N}^{+} \mathrm{~Cl}^{-}\), show no evidence for increased ice-like structure compared to pure water [36]. Nevertheless thermodynamic and transport properties generally point to the conclusion that the ion \(\mathrm{Me}_{4} \mathrm{~N}^{+}\) does not promote near-neighbor water-water hydrogen bonding [37,38].
Footnotes
[1] J. D. Bernal and R. H. Fowler, J.Chem.Phys.,1933, 1 ,515.
[2] See for example, P. A. Kollman and L. C. Allen, Chem. Rev.,1972, 72 ,283.
[3] E. J. Verwey, Rec. Trav. Chim.,1942, 61 ,127.
[4] See also F. Vaslow, J. Phys.Chem.,1973, 67 ,2773.
[5] C. M. Criss, J. Phys. Chem.,1974, 78 ,1000.
[6] K. K. Kundu, Pure Appl. Chem.,1994, 66 ,411.
[7] H. S. Frank and M. W. Evans, J. Chem. Phys.,1945, 13 ,507.
[8] J. E. Enderby, Chem.Soc.Rev.,1995, 24 ,159.
[9] G. W. Neilson and J. E. Enderby, Adv.Inorg.Chem.,1989, 34 ,195; and references therein.
[10] J. E. Enderby and G.W. Neilson in Water A Comprehensive Treatise; ed.F. Franks, Plenum Press, New York, 1973,volume 6, chapter 1.
[11] H. S. Frank and W.-Y. Wen, Discuss Faraday Soc.,1957,24,756.
[12] W.-Y.Wen,in Ions and Molecules in Solution; ed. N. Tanaka, H. Otaki and R. Tamamushi, Elsevier, Studies in Physical and Theoretical Chemistry, Amsterdam, 1983, p.45.
[13] G. Beurskens and G. A. Jeffrey, J.Chem.Phys.,1964, 41 ,917 and 924.
[14] P. Kebarle in Modern Aspects of Electrochemistry, ed.B.E.Conway and J. O’M. Bockris, 1974, 9 ,1; and references therein
[15] H. S. Frank, J. Phys Chem.,1963, 67 ,1554.
[16] E. M. Arnett and J. J. Campion, J.Am.Chem.Soc.,1970, 92 ,7097.
[17] K. Tamaki, S. Yoshikawa and M. Kushida, Bull. Chem. Soc. Jpn., 1975, 48 ,3018.
[18] G. A. Jeffrey, Prog. Inorg. Chem., 1967, 8 ,43; and references therein
[19] D. Feil and G. A. Jeffrey, J.Chem.Phys.,1961,35,1863.
[20] C. Shin, I. Worsley and C.M. Criss, J. Solution Chem.,1976, 5 ,867.
[21] S. Lindebaum, J. Phys. Chem.,1971, 75 ,3733; and references therein
[22] P.-A. Leduc and J. E. Desnoyers, Can. J. Chem.,1973, 51 ,2993.
[23] S. Lindenbaum, J.Chem.Thermodyn.,1971, 3 ,625.
[24] A. H. Narten and S. Lindenbaum., J. Chem. Phys.,1969, 51 ,1108.
[25] R. H. Boyd, J. Chem.Phys.,1969, 51 ,1470.
[26] O. D. Bonner and C. F. Jumper, Infrared Physics, 1973, 13 ,233.
[27] R. L. Kay, Adv. Chem. 1968, 73 ,1
[28] T. S. Sarma and J. C. Ahluwalia, J. Phys. Chem.,1970, 74 ,3547.
[29] T. S. Sarma, R. K. Mohanty and J. C. Ahluwalia, Trans. Faraday Soc.,1969, 65 ,2333.
[30] D. A. Johnson and J. F. Martin, J. Chem. Soc. Dalton, Trans.,1973,1585.
[31] T. S. Sunder, B. Chawla and J. C. Ahluwalia, J. Phys. Chem.,1974, 78 , 738.
[32] E. M. Arnett, M. Ho and L. L. Schaleyer, J.Am. Chem. Soc.,1970, 93 ,77039.
[33] A. LoSurdo, W.-Y. Wen, C. Jolicoeur and J.-L.Fortier,J.Phys.Chem.,1977, 81 , 1813;and references therein.
[34] W.-Y. Wen and S. Saito, J.Phys.Chem.,1965, 69 ,3569.
[35] G.P. Cunningham, D.F. Evans and R.L. Kay, J.Phys.Chem.,1966,70,3998.
[36] J. Turner, A.K. Soper and J.L. Finney, Mol.Phvs.,1992,77,411.
[37] R. L. Kay, D. F. Evans and M.A. Matesich, in Solute-Solute Interactions, ed. J. F. Coetzee and C. D. Ritchie, Marcel Dekker, New York, 1976,voume.2, chapter 10.
[38] R. L. Kay, Water A Comprehensive Treatise, ed. F. Franks, Plenum Press, New York, 1973, volume 3, chapter 4.